Butterfly velocity bound and reverse isoperimetric inequality
Abstract
We study the butterfly effect of the AdS planar black holes in the framework of Einstein's general relativity. We find that the butterfly velocities can be expressed by a universal formula v_{B}^{2}=T S /(2 V_{th}P ). In doing so, we come upon a nearhorizon geometrical formula for the thermodynamical volume V_{th} . We verify the volume formula by examining a variety of AdS black holes. We also show that the volume formula implies that the conjectured reverse isoperimetric inequality follows straightforwardly from the nullenergy condition, for static AdS black holes. The inequality is thus related to an upper bound of the butterfly velocities.
 Publication:

Physical Review D
 Pub Date:
 March 2017
 DOI:
 10.1103/PhysRevD.95.066001
 arXiv:
 arXiv:1701.05204
 Bibcode:
 2017PhRvD..95f6001F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Latex, 25 pages, typos corrected and references added. Further discussion on black hole volume as a quantity in addition to T and S to specify the nearhorizon geometry